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Probability Models in Electrical and Computer Engineering | |
Mathematical models as tools in analysis and design | |
Deterministic models | |
Probability models | |
Statistical regularity | |
Properties of relative frequency | |
The axiomatic approach to a theory of probability | |
Building a probability model | |
A detailed example: a packet voice transmission system | |
Other examples | |
Communication over unreliable channels | |
Processing of random signals | |
Resource sharing systems | |
Reliability of systems | |
Overview of book | |
Summary | |
Problems | |
Basic Concepts of Probability Theory | |
Specifying random experiments | |
The sample space | |
Events | |
Set operations | |
The axioms of probability | |
Discrete sample spaces | |
Continuous sample spaces | |
Computing probabilities using counting methods | |
Sampling with replacement and with ordering | |
Sampling without replacement and with ordering | |
Permutations of n distinct objects | |
Sampling without replacement and without ordering | |
Sampling with replacement and without ordering | |
Conditional probability | |
Bayes' Rule | |
Independence of events | |
Sequential experiments | |
Sequences of independent experiments | |
The binomial probability law | |
The multinomial probability law | |
The geometric probability law | |
Sequences of dependent experiments | |
A computer method for synthesizing randomness: random number generators | |
Summary | |
Problems | |
Random Variables | |
The notion of a random variable | |
The cumulative distribution function | |
The three types of random variables | |
The probability density function | |
Conditional cdf's and pdf's | |
Some important random variables | |
Discrete random variables | |
Continuous random variables | |
Functions of a random variable | |
The expected value of random variables | |
The expected value of X. The expected value of Y = g(X). Variance of X | |
The Markov and Chebyshev | |
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